The Quest unlocks the Puppy Pal and Internet Kitten Hobbies, and new outfits for Puppies and Kittens in the Pet Salon.
You have 7 Days to do the Puppy Pals Hobby Event once the Puppy Odyssey is over, if you want to ad a Poodle to the Pets collection. When you've collected all 12 items you will get themed clothes for your sims.
The Internet Kitten hobby is without time limit and unlocks the Persian Cat Breed when you've collected the 12 items.
You will have to buy a Puppy Playmat and Kitten Play Box, §1.000 each, in the Promotins R'Us Store to do the Hobbies.

Will do. I was foolishly excited to be able to try out the different collars on my sim pooches. (In real life I have three sheepdogs but a ridiculous number of collars and leads. There are so many cute ones to buy. Meanwhile the dogs themselves wouldn't care if they had just one half-chewed one each, just so long as they get their two hours of running/mooching every day)